-6x – 4y = -14
4x – 12y = -20

a. (1, 2)
b. (-2, 1)
c. (-2,4)
d. (-2,-4)

A.(1,2)

Step-by-step explanation:

Step: Substitute

−2 /3 y +  7 /3

4x−12y=−20:

4x−12y=−20

4( −2 /3 y +  7 /3 )−12y=−20

-44/3y +  28 /3 =−20(Simplify both sides of the equation)

−44 /3 y +  28 /3  +  −28 /3  =−20+  −28 /3

(Add (-28)/3 to both sides)

−44 /3 y=  −88 /3

−44 /3 y

−44 /3 =  −88 /3  −44 /3

(Divide both sides by (-44)/3)

y=2

Step: Substitute2foryinx=

−2 /3 y+ 7 /3 :

x= −2 /3 y+ 7 /3

x= −2 /3 (2)+ 7 /3

x=1(Simplify both sides of the equation)

x=1 and y=2

blue marble is 15 times out of 50 = 15/50 reduces to 3/10

landing on tails is 24 out of 50 = 24/50 reduces to 12/25

to find the probability of both multiply together:

3/10 x 12/25 = 3 x 12 / 10 x 25 = 36/250

if you multiplied the numerator and denominator by 10 you get 360/2500.

the answer is 360/2500

answer: ratio of volume of cone (with 3 times the height and equal diameter) to volume of cylinder is 2 to 1. the value of π is not used.

step-by-step explanation:

radius is diameter/2 = 4.

area of circle is π r^2.

volume of cylinder is height × area of base = hπr^2 = 3(4^2) π = 48π cubic inches.

not knowing the formula for volume of cone, i calculate it using calculus (which is for calculating things).

volume of cone is integral 0 to h area(y) dy. area(y) is π r(y)^2. r(y) runs r to zero as y runs zero to h, r(0) = r, r(h) = 0.

r(y) = r - r/h y

area(y) = π (r - r/h y)^2 = π (r^2 - 2r^2y/h + r^2y^2/h^2) = π r^2(1-2y/h+y^2/h^2)

antiderivative area(y) = π r^2 (y-y^2/h+y^3/(3h^2))

integral 0 to h = π r^2(h-h^2/h+h^3/(3h^2) - (0)) = π r^2(h - h + h/3) = π r^2(h/3) = π/3 r^2 h

volume of this cone is π/3(4^2)18 cubic inches.

= 6 16 π = 96π cubic inches.

cone has twice the volume, 96/48.

cone height is 6 times the cylinder.

ratio of volume formula: π r^2 cancels.

cone over cylinder ratio is 6h/3 to h, 2 to 1.